Proceedings of the American Mathematical Society

Author(s): R. S. Laugesen
Journal: Proc. Amer. Math. Soc. 135 (2007), 211-216.
MSC (2000): Primary 42C40; Secondary 42C15
Posted: June 29, 2006
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Abstract: We answer a question of O. Christensen about affine systems in $L^2(\mathbb{R})$ . Specifically, we show that if the dilation factor

is transcendental, then cancellations cannot occur between different scales, in the conditions for the affine system to form a frame. Such cancellations are known to occur when

is an integer.

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Retrieve articles in Proceedings of the American Mathematical Society with MSC (2000): 42C40, 42C15

R. S. Laugesen
Affiliation: Department of Mathematics, University of Illinois, Urbana, Illinois 61801
Email: Laugesen@uiuc.edu

DOI: 10.1090/S0002-9939-06-08456-5
PII: S 0002-9939(06)08456-5
Keywords: Affine system, frame, transcendental
Received by editor(s): June 30, 2005
Received by editor(s) in revised form: July 31, 2005
Posted: June 29, 2006
Additional Notes: This work was completed during a Visiting Erskine Fellowship at the University of Canterbury, New Zealand, and also with support from National Science Foundation award DMS--0140481.
Communicated by: Joseph A. Ball
Copyright of article: Copyright 2006, American Mathematical Society
The copyright for this article reverts to public domain after 28 years from publication.

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